Final Answer:
The triangles are similar due to the Angle-Angle (AA) criterion.
Step-by-step explanation:
The given triangles are determined to be similar based on the Angle-Angle (AA) criterion. Both triangles share an angle of 30°, and another angle of 109°, establishing the angle-angle correspondence required for similarity.
According to the AA criterion, if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. In this case, the angles 30° and 109° in the first triangle correspond to the angles 30° and 109° in the second triangle, satisfying the AA criterion.
It's important to note that the Side-Angle-Side (SAS) and Side-Side-Side (SSS) criteria are not applicable here.
While both triangles share angles, there is no given information about corresponding sides or a combination of angles and sides that satisfy the SAS or SSS criteria. Therefore, these criteria cannot be used to establish similarity in this particular scenario.
In conclusion, the triangles are indeed similar, and the reason for their similarity is the Angle-Angle (AA) criterion, as the given angles in one triangle correspond to the angles in the other triangle.
This provides a sufficient basis for establishing similarity without the need for information about the lengths of the sides.